Direct formulation to Cholesky decomposition of a general nonsingular correlation matrix

We present two novel, explicit representations of Cholesky factor of a nonsingular correlation matrix. The first representation uses semi-partial correlation coefficients as its entries. The second, uses an equivalent form of the square roots of the differences between two ratios of successive determinants. Each of the two new forms enjoys parsimony of notations and offers a simpler alternative to both spherical factorization and the multiplicative partial correlation Cholesky matrix (Cooke et al 2011). Two relevant applications are offered for each form: a simple $t$-test for assessing the independence of a single variable in a multivariate normal structure, and a straightforward algorithm for generating random positive-definite correlation matrix. The second representation is also extended to any nonsingular hermitian matrix.Comment: Accepted to Statistics and Probability Letters, March 201

Direct formulation of a 4-node hybrid shell element with rotational degrees of freedom

A simple 4-node assumed-stress hybrid quadrilateral shell element with rotational or drilling degrees of freedom is formulated. The element formulation is based directly on a 4-node element. This direct formulation requires fewer computations than a similar element that is derived from an internal 8-node isoparametric element in which the midside degrees of freedom are eliminated in favor of rotational degree of freedom at the corner nodes. The formulation is based on the principle of minimum complementary energy. The membrane part of the element has 12 degrees of freedom including rotational degrees of freedom. The bending part of the element also has 12 degrees of freedom. The bending part of the quadratic variations for both in-plane and out-of-plane displacement fields and linear variations for both in-plane and out-of-plane rotation fields are assumed along the edges of the element. The element Cartesian-coordinate system is chosen such as to make the stress field invariant with respect to node numbering. The membrane part of the stress field is based on a 9-parameter equilibrating stress field, while the bending part is based on a 13-parameter equilibrating stress field. The element passes the patch test, is nearly insensitive to mesh distortion, does not lock, possesses the desirable invariance properties, has no spurious modes, and produces accurate and reliable results

Condition number estimates for combined potential boundary integral operators in acoustic scattering

We study the classical combined field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle, namely the indirect formulation due to Brakhage-Werner/Leis/Panic, and the direct formulation associated with the names of Burton and Miller. We obtain lower and upper bounds on the condition numbers for these formulations, emphasising dependence on the frequency, the geometry of the scatterer, and the coupling parameter. Of independent interest we also obtain upper and lower bounds on the norms of two oscillatory integral operators, namely the classical acoustic single- and double-layer potential operators

Direct formulation of the supersonic acoustic intensity in space domain

International audienceThis paper proposes and examines a direct formulation in space domain of the so-called supersonic acoustic intensity. This quantity differs from the usual (active) intensity by excluding the circulating energy in the near-field of the source, providing a map of the acoustic energy that is radiated into the far field. To date, its calculation has been formulated in the wave number domain, filtering out the evanescent waves outside the radiation circle and reconstructing the acoustic field with only the propagating waves. In this study, the supersonic intensity is calculated directly in space domain by means of a two-dimensional convolution between the acoustic field and a spatial filter mask that corresponds to the space domain representation of the radiation circle. Therefore, the acoustic field that propagates effectively to the far field is calculated via direct filtering in space domain. This paper presents the theory, as well as a numerical example to illustrate some fundamental principles. An experimental study on planar radiators was conducted to verify the validity of the technique. The experimental results are presented, and serve to illustrate the usefulness of the analysis, its strengths and limitations

Decoupling Limits of sGoldstino Modes in Global and Local Supersymmetry

We study the decoupling limit of a superheavy sgoldstino field in spontaneously broken N=1 supergravity. Our approach is based on K\"ahler superspace, which, among others, allows direct formulation of N=1 supergravity in the Einstein frame and correct identifications of mass parameters. Allowing for a non-renormalizable K\"ahler potential in the hidden sector, the decoupling limit of a superheavy sgoldstino is identified with an infinite negative K\"ahler curvature. Constraints that lead to non-linear realizations of supersymmetry emerge as consequence of the equations of motion of the goldstino superfield when considering the decoupling limit. Finally, by employing superspace Bianchi identities, we identify the real chiral superfield, which will be the superconformal symmetry breaking chiral superfield that enters the conservation of the Ferrra-Zumino multiplet in the field theory limit of N=1 supergravity.Comment: 15 pages, version to be published in Phys. Lett.